Condensation energy in strongly coupled superconductors

We consider the condensation energy E_c of strongly coupled magnetically mediated superconductors within the context of the spin-fermion model. We argue that the actual physics behind the condensation energy is much richer than in BCS theory, and that it is vital to take both the fermionic and bosonic contributions to the condensation energy into account. We argue that at strong coupling λ ≫ 1, the gain in the condensation energy is a result of the feedback on spin excitations, while the fermionic contribution to E_c is positive due to an “undressing” feedback on the fermions. In addition we argue that the same feedback effect accounts for a gain in the kinetic energy at strong coupling. We also found that the BCS relation E_c ∝ Δ², where Δ is the pairing gap, only holds for λ < ∼1. At larger λ, Δ keeps increasing and eventually saturates, while E_c passes through a maximum at λ ∼ 2 and then exhibits a decrease in the strong-coupling regime.